Question: Multiply and simplify the following complex numbers: $({-3-2i}) \cdot ({-4+2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-2i}) \cdot ({-4+2i}) = $ $ ({-3} \cdot {-4}) + ({-3} \cdot {2i}) + ({-2i} \cdot {-4}) + ({-2i} \cdot {2i}) $ Then simplify the terms: $ (12) + (-6i) + (8i) + (-4i^2) $ Imaginary unit multiples can be grouped together. $ 12 + (-6 + 8)i - 4 i^2 $ After we plug in $i^2 = -1$, the result becomes $ 12 + (-6 + 8)i - (-4) $ The result is simplified: $ (12 + 4) + (2i) = 16+2i $